1.4 "The teaching and learning of Mathematics aims to develop a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations" (DBE 2011, p.8). Design an activity that could help learners recognise that percentages can be applied across social situations (relating to activities in real life) and fully explain how you would use it in teaching and learning. ​

Answer:

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

To solve this problem, we can use the following formula:

(amount of solution 1) + (amount of solution 2) = total amount of mixture

We can also set up equations for the amount of acid in each of the solutions:

0.25(amount of solution 1) + 0.65(amount of solution 2) = 0.4(total amount of mixture)

We have two equations and two unknowns, so we can solve for the amounts of each solution. Let's set x to be the amount of the 25% acid solution and y to be the amount of the 65% acid solution. Then we have:

x + y = 80                (equation 1)

0.25x + 0.65y = 0.4(80)   (equation 2)

We can simplify equation 2 by multiplying everything by 100, to get rid of the decimals:

25x + 65y = 3200

Now we can solve this system of equations. One way to do this is to solve equation 1 for one of the variables, and substitute it into equation 2. We get:

x = 80 - y

25(80 - y) + 65y = 3200

2000 - 25y + 65y = 3200

40y = 1200

y = 30

So we need 30 liters of the 65% acid solution. To find the amount of the 25% acid solution, we can substitute y = 30 into equation 1:

x + 30 = 80

x = 50

So we need 50 liters of the 25% acid solution. Therefore, we need 50 liters of the 25% acid solution and 30 liters of the 65% acid solution to produce 80 liters of a 40% acid solution.

The minimum number of extra squares that need to be shaded so that the pattern has rotational symmetry of order is 3

From the question, we have the following parameters that can be used in our computation:

The composite figure

On the extension at the left-hand side of the figure, we can see that

The shaded shape is a rectangle while other shaded shapes are squares

This means that the other shaded squares must be extended to form a rectangle

There are three of the squares that can be extended to rectangles

Hence, the minimum number of squares is 3

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The required heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.

The heat energy required to boil a substance can be calculated using the formula:

Q = m × Hv

where Q is the heat energy, m is the mass of the substance, and Hv is the heat of vaporization. From the given, we have m = 75.25 g and Hv = 0.826 kJ/g

Substituting the given values, we get:

Q = 75.25 g × 0.826 kJ/g

Q = 62.1835 kJ

Where kJ (kilojoule) is the unit of heat.

Therefore, the heat energy required to boil 75.25 g of ethanol is 62.1835 kJ.

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The number of fish, including angelfish and eels that are shown by the bar graph, can be found to be 45 fish .

The science museum water exhibit bar graph shows the number of animals that are in the water exhibit in the museum.

We see that there are 15 snakes, 10 Turtles, 25 Angelfish, and 20 eels.

If we are to find the number of fish in the science museum water exhibit, all we need to do is to sum up the number of Angelfish and Eels. Doing this sum would add up to :

= 25 Angelfish + 20 eels

= 45 fish

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When C = 20, F is equal to 68, and when F = 100, C is approximately 37.78.

Given the equations:

C = (5/nine) * (F - 32)

F = (9/5) * C + 32

If we replace specific values for F or C, we will locate the corresponding price for the opposite variable. Here are some examples:

Let's expect C = 20. Substituting this fee into the second equation:

F = (9/five) * 20 + 32

F = 36 + 32

F = 68

Therefore, when C = 20, F is equal to sixty-eight.

Let's expect F = a hundred. Substituting this cost into the primary equation:

C = (five/9) * (100 - 32)

C = (5/9) * 68

C = 340/9

C ≈ 37.78

So, whilst F = one hundred, C is approximately 37.78.

These examples exhibit how you may locate the values of F and C by using substituting one variable into the equations and fixing for the alternative variable. Remember, you could choose any unique values for F or C and perform the calculations consequently.

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The correct question is:

"C=5/9 (f -32)

F= 9/5C + 32

Solve for F and C"

Based on the given figures, the most likely transformation that maps figure ABCD onto figure A'B'C'D' is option A, reflection across the Y-axis.

This is because the x-coordinates of the corresponding points in the two figures are opposite to each other when reflected across the Y-axis.  

A rotation of 90⁰ clockwise or counter-clockwise about the origin would result in the image being in a different quadrant, and a rotation of 180° about the origin would place the image on the opposite side of the origin.

A translation would move the image to a different location without changing its orientation, but there is no indication in the question that a translation is a possible transformation. Hence it's a reflection across Y-axis.

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Correct Question

(Image Attached)

In order to break even, either 5 cameras or 6 cameras must be produced and sold.

At break-even point, revenue (R) equal is set to equal the cost (C)

Given that:

R = 24x - x².

C = 30 + 13x.

where

R is revenue and

C is the cost

Setting R equal to C:

24x - x² = 30 + 13x

Rearranging the equation:

x² - 11x + 30 = 0

Now, we can solve this quadratic equation to find the break-even point(s).

Factoring the quadratic equation:

(x - 6)(x - 5) = 0

Setting each factor equal to zero:

x - 6 = 0  ==> x = 6

x - 5 = 0  ==> x = 5

Therefore, the break-even point occurs when x = 6 or x = 5.

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The volume of the rectangular pyramid is 20800 m³.

The volume of the pyramid can be found as follows:

The pyramid is a rectangular base pyramid. Therefore,

volume of the pyramid = 1 / 3 Bh

where

Therefore,

B = 52 × 30

B = 1560 m²

volume of the pyramid = 1 / 3 × 1560 × 40

volume of the pyramid = 62400 / 3

volume of the pyramid = 20800 m³

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(C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year is correct option.

Both Investment A and Investment B are annuities, but we need to determine which one is an ordinary annuity. An ordinary annuity is one in which payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period.

Looking at the table, we can see that Investment A and Investment B both have payments made at the end of each month, so they are both examples of ordinary annuities.

To calculate the future value of each annuity after one year, we can use the formula:

[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]

where:

FV is the future value of the annuity

P is the payment amount

r is the interest rate per period (in this case, 3.5% per month)

n is the number of periods (12 in this case, since we're looking at one year)

For Investment A, we have P = 350, r = 0.035, and n = 12. Plugging these values into the formula, we get:

FV = 350 × [(1 + 0.035[tex])^12[/tex] - 1] / 0.035

= 3,906.64

Therefore, the answer is (C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year.

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The appropriate measure of variability for this data is the IQR, and its value is 250.

We have,

The range is not the best measure of variability for this data since it only takes into account the maximum and minimum values and does not consider the other values in the dataset.

The IQR (interquartile range) is a better measure of variability since it gives a measure of the spread of the middle 50% of the data.

To find the IQR, we first need to find the median:

Arranging the data in order, we get:

200, 450, 600, 650, 700, 800

The median is the middle value, which is 650.

The first quartile (Q1) is the median of the lower half of the data:

Q1 = median(200, 450, 600) = 450

The third quartile (Q3) is the median of the upper half of the data:

Q3 = median(700, 800, 650) = 700

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

= 700 - 450

= 250

Therefore,

The appropriate measure of variability for this data is the IQR, and its value is 250.

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The possible equation for Nate's line is C) 6x - 5y = 15.

To find the equation of the line perpendicular to Maria's line, we need to determine the slope of Maria's line first.

Maria's line is represented by the equation:

y = -5/6 x + 8

The slope of this line can be determined by comparing it to the slope-intercept form of a linear equation (y = mx + b), where m is the slope. Thus, the slope of Maria's line is -5/6.

The slope of a line perpendicular to Maria's line will be the negative reciprocal of -5/6, which is 6/5.

Therefore, the equation of Nate's line could be in the form:

y = 6/5 x + b

where b is the y-intercept of Nate's line.

To determine which of the given answer choices is the equation of Nate's line, we can substitute the equation y = 6/5 x + b into each answer choice and see which one holds true.

A) 5x - 6y = 15

Substituting y = 6/5 x + b, we get:

5x - 6(6/5 x + b) = 15

5x - 36/5 x - 6b = 15

-11/5 x - 6b = 15

This equation is not equivalent to y = 6/5 x + b, so A is not the answer.

B) 5x + 6y = 15

Substituting y = 6/5 x + b, we get:

5x + 6(6/5 x + b) = 15

5x + 36/5 x + 6b = 15

46/5 x + 6b = 15

This equation is not equivalent to y = 6/5 x + b, so B is not the answer.

C) 6x - 5y = 15

Substituting y = 6/5 x + b, we get:

6x - 5(6/5 x + b) = 15

6x - 6x - 5b = 15

-5b = 15

b = -3

This equation is equivalent to y = 6/5 x - 3, so C could be the answer.

D) 6x + 5y = 15

Substituting y = 6/5 x + b, we get:

6x + 5(6/5 x + b) = 15

6x + 6x + 5b = 15

12x + 5b = 15

This equation is not equivalent to y = 6/5 x + b, so D is not the answer.

Therefore, the possible equation for Nate's line is C) 6x - 5y = 15.

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The value of the y-intercept of the graph of the function h(x) = 12.3(4.9)^x is 12.3.

To determine the value of the y-intercept of the graph of the function[tex]h(x) = 12.3(4.9)^x,[/tex] we need to find the value of h(0) since the y-intercept corresponds to the point where the graph intersects the y-axis (x = 0).

Substituting x = 0 into the function, we have:

[tex]h(0) = 12.3(4.9)^0[/tex]

Since any number raised to the power of 0 is equal to 1, we have:

h(0) = 12.3(1)

Multiplying 12.3 by 1 gives us:

h(0) = 12.3

Therefore, the value of the y-intercept of the graph of [tex]h(x) = 12.3(4.9)^x[/tex] is 12.

The y-intercept represents the value of the function when x = 0, which in this case is 12.3.

It is the point where the graph crosses the y-axis.

This means that when there is no exponential growth or decay (x = 0), the value of the function is 12.3. As x increases or decreases, the function will grow or decay exponentially, but at x = 0, it starts with a value of 12.3.

The graph of this function would start at the point (0, 12.3) and then either increase or decrease exponentially depending on the value of the base (4.9 in this case).

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Solving a linear equation we can see that the smallest number is 5.

A set of 3 consecutive odd numbers can be written as:

x, x + 2, and x + 4

the middle one is x + 2, and we know that 4 times the second must be equal to the sum of the other two plus 14, then we can write the linear equation:

4*(x + 2) = x + x + 4 + 14

Solving this linear equation we will get:

4x + 8 = 2x + 18

4x -2 x=  18 - 8

2x = 10

dividing both sides by 2, we will get:

x = 10/2

x = 5

That is the smalles odd number.

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The probability of randomly selecting an apartment unit that has both internet and cable connection on the second floor = 0.23

Given that,

For second floor:

Total outcomes = 40

Network preference of internet & cable both = 9

Then Favorable outcomes = 9

Since we know that,

Probability is the ratio of number of favorable outcomes and total number of outcomes. It deals with finding out the likelihood of the occurrence of an event.

Therefore, to find the probability that,

P(Randomly selecting an apartment unit having internet and cable both )

= 9/40

= 0.225

≈ 0.23

Thus, the required probability = 0.23

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Answer:

First, let's calculate the total cost of buying the shares:

1000 shares * $15.23/share = $15,230

Next, we need to calculate the commission paid to the broker for buying the shares:

$15,230 * 0.0075 = $114.23

So, the total cost of buying the shares including the commission is:

$15,230 + $114.23 = $15,344.23

Now, let's calculate the total revenue from selling the shares:

1000 shares * $18.78/share = $18,780

We also need to calculate the commission paid to the broker for selling the shares:

$18,780 * 0.0075 = $140.85

So, the total revenue from selling the shares after the commission is:

$18,780 - $140.85 = $18,639.15

The total profit from buying and selling the shares is:

$18,639.15 - $15,344.23 = $3,294.92

The rate of return is the profit divided by the total cost, expressed as a percentage:

($3,294.92 / $15,344.23) * 100% = 21.5%

Therefore, Omar's rate of return is 21.5%.

Answer:

The answer is -4.4.

Step-by-step explanation:

First, you have to add -12 + -10 + -6 and it equals -28. Next add the positive numbers 4+ 2 equals 6. Then, put them altogether meaning -28 + 6 equals -22, then divide it by the number of players which is 5 then you get the answer of -4.4.

Have a nice day.

The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

We have,

Let's assume the weight of a large box is L kg, and the weight of a small box is S kg.

According to the given information, we can create the following equations:

Equation 1: 3L + 5S = 135 (1st delivery)

Equation 2: 9L + 7S = 279 (2nd delivery)

To solve these equations, we can use a method called "elimination" or "substitution."

Multiply Equation 1 by 3 and Equation 2 by 1, so that the coefficients of L will be the same:

Equation 1: 9L + 15S = 405

Equation 2: 9L + 7S = 279

Now, we can subtract Equation 2 from Equation 1 to eliminate L:

(9L + 15S) - (9L + 7S) = 405 - 279

Simplifying:

8S = 126

Divide both sides of the equation by 8:

S = 126/8 = 15.75

So, the weight of a small box (S) is 15.75 kg.

Now,

substitute the value of S into Equation 1 to find the weight of a large box (L):

3L + 5(15.75) = 135

3L + 78.75 = 135

3L = 135 - 78.75

3L = 56.25

Divide both sides of the equation by 3:

L = 56.25/3 = 18.75

So,

The weight of a large box (L) is 18.75 kg.

Thus,

The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

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The meaning of the statement is if you take n distinct numbers, x₁, ..., xₙ, and permute them in all possible ways, the number of different values that the function f(x₁, ..., xₙ) can take on will be a divisor of n!.

This assertion is a specific instance of a broader concept known as the Principle of Inclusion-Exclusion in the field of combinatorics. The Principle of Inclusion-Exclusion asserts that when dealing with a set comprising n elements and aiming to determine the number of possible subsets that can be selected, one can arrive at this figure by summing up the number of options for choosing 0, 1, 2, and up to n elements from the set.

Regarding the aforementioned assertion, the collection of components comprises every potential arrangement of the numerical values x₁, ..., xₙ. There is only one possible way to choose 0 elements, there are n options for choosing 1 element, selecting 2 elements can be done in n(n-1)/2 ways, and the pattern continues.

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The three statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   .......equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

Based on the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

By comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x - 0)² + (y - 0)² = 3²

x² + y² = 9.

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Complete Question:

Consider a circle whose equation is x² + y² – 2x – 8 = 0. Which statements are true? Select three options.

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The center of the circle lies on the y-axis.

The standard form of the equation is (x – 1)² + y² = 3.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answer:

720 m^2

Step-by-step explanation:

Solution:

The formula for the surface area of a triangular prism is:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

where,

Given:

side 1 (S1) : 5 m

side 2(S2): x m

side 3(S3): 12 m

length (l)=22m

Here we need to find side 2, we can easily find it using Pythagoras' theorem.

a^2+b^2=c^2

5^2+12^2=x^2

x^2=169

x=[tex]\sqrt{169}=13 m[/tex]

therefore, side 2 is 13 m.

Substituting value in the formula

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

Surface Area=(5+13+12)*22+5*12= 720 m^2

Answer:

720 m²

Step-by-step explanation:

The given diagram shows a triangular prism.

A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.

To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:

[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]

The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:

[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]

Therefore, the total surface area of the given triangular prism is 720 m².

The graph of the inequality is attached in the solution.

Given is an inequality, 2y > x-2, we need to graph it,

So, considering this as, 2y = x-2

Solving like a linear equation to get the points to plot,

So,

Put y = 0,

0 = x - 2

x = 2

(2, 0)

Put x = 0,

2y = 0-2

y = -1

(0, -1)

Hence the two points from which the graph will pass are (2, 0) and (0, -1).

Now, since the inequality has a > sign so the shaded area will be above the line and the line will be dotted.

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Daisy would be paid $155 if she works 13 hours in a day.

If Daisy works for up to 8 hours in a day, she is paid a flat rate of $10 per hour, so her earnings for the day would be:

Earnings = 10 × 8 = $8

If Daisy works for more than 8 hours in a day, then her earnings for the extra hours are calculated at a rate of 1.5 times her hourly wage, which is $15 per hour.

So, if Daisy works x hours in a day, where x is greater than 8, then her net earnings for the day can be expressed as:

Earnings = 80 + (x - 8) × 15

This expression takes into account the first 8 hours of work, which are paid at a flat rate of $10 per hour, and the extra hours, which are paid at a rate of $15 per hour

If Daisy works 13 hours in a day, then her net earnings for the day would be:

Earnings = 80 + (13 - 8) × 15 = 80 + 5 × 15 = $155

So Daisy would be paid $155 if she works 13 hours in a day.

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Answer:

121

Step-by-step explanation:

firstly you arrange the numbers in ascending order the number in the middle is considered to be the median

Entertainment will comprise 90% of Ryan's total budget. He will allocate 90% of his monthly income towards entertainment expenses.

According to the given information:

Let's assume Ryan's take-home pay is P dollars.

Assuming that Ryan puts aside 10% of his net income for his retirement plan, he will accumulate savings of 0.10P dollars.

After setting aside funds for retirement, the remaining portion of his net earnings will constitute 90% of the original amount, equating to 0.90P dollars.

Assuming that Ryan puts the remaining amount of his income towards entertainment, it is possible to determine the proportion of his overall expenses that entertainment would represent.

Percentage of entertainment budget = (Entertainment budget / Total budget) * 100

Given an overall budget of P dollars, with 0.90P dollars allotted for entertainment expenses, the proportion of the total budget that will be spent on entertainment can be calculated as a percentage.

Percentage of entertainment budget = (0.90P / P) * 100

Percentage of entertainment budget = 90%

So, entertainment will comprise 90% of Ryan's total budget.

He will allocate a monthly entertainment budget of 0.90P dollars, equivalent to 90% of his salary after taxes.

As such, the overwhelming majority of Ryan's budget will be allocated towards Entertainment. Every month, the entertainment allowance will constitute 90% of his net income as per the allocated budget.

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The value of y at the indicated point is √3.

In Mathematics and Geometry, a square root function refers to a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In this scenario and exercise, we would determine the y-value by substituting the x-value into the given square root function as follows;

y² = x - 3

By taking the square root of both sides of the square root function, we have:

y = √(x - 3)

When x = 6, the y-value is given by;

y = √(6 - 3)

y = √3

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Answer:

where do you live

Step-by-step explanation:

If the flow rate of the tap is reduced to 7 litres per minute, it would take 36 hours to fill the reservoir.

Let's use the formula:

time = volume/flow rate

where volume is the volume of the reservoir and flow rate is the flow rate of the tap.

Let V be the volume of the reservoir.

With a flow of 18 litres per minute, we have:

14 hours = V / 18 L/min

Solving for V, we get:

V = 14 hours x 18 L/min = 252 L

Now, let's find the time it takes to fill the same reservoir with a flow of 7 litres per minute:

time = V / 7 L/min

Substituting V with 252 L, we get:

time = 252 L / 7 L/min = 36 hours

Therefore, it will take 36 hours to fill the reservoir with a flow rate of 7 litres per minute.

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Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

Holden drinks 1/8 gallon of water every 2 miles, so after hiking 14 miles, he would have drank (14/2) * (1/8) = 7/16 gallons of water.

Melissa drinks 3/8 gallon of water every 2 miles, so after hiking 14 miles, she would have drank (14/2) * (3/8) = 21/32 gallons of water.

The difference in the amount of water they drink is:

21/32 - 7/16 = 21/32 - 14/32 = 7/32 gallons

Therefore, Melissa will drink 7/32 gallons more water than Holden after hiking 14 miles.

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Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation: